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Optimization Algorithm Improved with Potentially Widespread Impact

Category: Science & Technology
Posted: 06:26AM

The ability to optimize is invaluable for engineering and other fields, not only because of the results optimization can bring, but also because optimization algorithms can be very complex and hard to run. The problems can involve a large number of variables, and each one increases the dimensionality of the problem. One optimization approach is the 'cutting-plane' method and now researchers at MIT have devised a new form of it that is significantly faster, and may be applicable to more problems.

If you envision all possibilities for a system within a large circle, the optimal possibilities will be contained within a smaller circle. By picking a random point, you can determine if it is within the smaller circle, and if it is not, draw a line to that circle, cutting the larger circle in two. The cutting-plane method uses the same idea, but with more dimensions, or variables, and previous approaches required an amount of time proportional to the dimensionality raised to the power of 3.373. What the MIT researchers have done is brought that power down to just 3, which is a significant reduction when a large number of variables are in play. They have also figured out how to apply this approach to other systems, reducing the running times by multiple powers in some cases.

Beyond creating one improved optimization algorithm, the researchers hope that this one method can be applied to various problems. Currently different problems also have different optimization methods, so by using the same method in multiple places, improving that one method can have a larger effect.

Source: MIT

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